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IIT JEE 1983
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81
Duration
180 mins
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IIT-JEE Advance - Previous Year Papers
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81questions
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40
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38
46.9%
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81questions
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PYP
IIT JEE 1983
Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed. (Neglect air resistance)
PYP
IIT JEE 1983
The energy of the electron in the 3d-orbital is less than that in the 4s-orbital in the hydrogen atom.
PYP
IIT JEE 1983
If the letters of the word "Assassin" are written down at random in a row, the probability that no two S's occur together is $$1/35$$
PYP
IIT JEE 1983
Gamma rays are electromagnetic radiations of wavelengths of 10-6 to 10-5 cm
PYP
IIT JEE 1983
Linear overlap of two atomic p-orbitals leads to a sigma bond.
PYP
IIT JEE 1983
If $$X.A=0, X.B=0, X.C=0$$ for some non-zero vector $$X,$$ then $$\left[ {A\,B\,C} \right] = 0$$
PYP
IIT JEE 1983
The equation $$2{x^2} + 3x + 1 = 0$$ has an irrational root.
PYP
IIT JEE 1983
The derivative of an even function is always an odd function.
PYP
IIT JEE 1983
The ex-radii $${r_1},{r_2},{r_3}$$ of $$\Delta $$$$ABC$$ are H.P. Show that its sides $$a, b, c$$ are in A.P.
PYP
IIT JEE 1983
If $$\tan \,A = \left( {1 - \cos B} \right)/\sin B,$$ then $$tan2A = tan\,B$$.
PYP
IIT JEE 1983
Find three numbers $$a,b,c$$ between $$2$$ and $$18$$ such that
(i) their sum is $$25$$
(ii) the numbers $$2,$$ $$a, b$$ are consecutive terms of an A.P. and
(iii) the numbers $$b,c,18$$ are consecutive terms of a G.P.
(i) their sum is $$25$$
(ii) the numbers $$2,$$ $$a, b$$ are consecutive terms of an A.P. and
(iii) the numbers $$b,c,18$$ are consecutive terms of a G.P.
PYP
IIT JEE 1983
The straight line $$5x + 4y = 0$$ passes through the point of intersection of the straight lines $$x + 2y - 10 = 0$$ and $$2x + y + 5 = 0.$$
PYP
IIT JEE 1983
If $$x-r$$ is a factor of the polynomial $$f\left( x \right) = {a_n}{x^4} + ..... + {a_0},$$ repeated $$m$$ times $$\left( {1 < m \le n} \right)$$, then $$r$$ is a root of $$\left( x \right) = 0$$ repeated $$m$$ times.
PYP
IIT JEE 1983
If $$z = x + iy$$ and $$\omega = \left( {1 - iz} \right)/\left( {z - i} \right),$$ then $$\,\left| \omega \right| = 1$$ implies that, in the complex plane,
PYP
IIT JEE 1983
4.08 g of a mixture of BaO and an unknown carbonate MCO3 was heated strongly. The residue weighed 3.64 g. This was dissolved in 100 ml of 1 N HCl. The excess acid required 16 ml of 2.5 N NaOH solution for complete neutralization. Identify the metal M. (At wt. H = 1, C = 12, O = 16, Cl = 35.5, Ba = 138)
PYP
IIT JEE 1983
If one root of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the $$n$$-th power of the other, then show that
$$${\left( {a{c^n}} \right)^{{1 \over {n + 1}}}} + {\left( {{a^n}c} \right)^{{1 \over {n + 1}}}} + b = 0$$$
PYP
IIT JEE 1983
If $${\left( {1 + x} \right)^n} = {C_0} + {C_1}x + {C_2}{x^2} + ..... + {C_n}{x^n}$$ then show that the sum of the products of the $${C_i}s$$ taken two at a time, represented $$\sum\limits_{0 \le i < j \le n} {\sum {{C_i}{C_j}} } $$ is equal to $${2^{2n - 1}} - {{\left( {2n} \right)!} \over {2{{\left( {n!} \right)}^2}}}$$
PYP
IIT JEE 1983
Cards are drawn one by one at random from a well - shuffled full pack of $$52$$ playing cards until $$2$$ aces are obtained for the first time. If $$N$$ is the number of cards required to be drawn, then show that $${P_r}\left\{ {N = n} \right\} = {{\left( {n - 1} \right)\left( {52 - n} \right)\left( {51 - n} \right)} \over {50 \times 49 \times 17 \times 13}}$$ where $$2 \le n \le 50$$
PYP
IIT JEE 1983
m men and n women are to be seated in a row so that no two women sit together. If $$m > n$$, then show that the number of ways in which they can be seated is $$\,{{m!(m + 1)!} \over {(m - n + 1)!}}$$
PYP
IIT JEE 1983
$$A, B, C$$ are events such that
$$P\left( A \right) = 0.3,P\left( B \right) = 0.4,P\left( C \right) = 0.8$$
$$P\left( {AB} \right) = 0.08,P\left( {AC} \right) = 0.28;\,\,P\left( {ABC} \right) = 0.09$$
$$P\left( A \right) = 0.3,P\left( B \right) = 0.4,P\left( C \right) = 0.8$$
$$P\left( {AB} \right) = 0.08,P\left( {AC} \right) = 0.28;\,\,P\left( {ABC} \right) = 0.09$$
If $$P\left( {A \cup B \cup C} \right) \ge 0.75,$$ then show that $$P$$ $$(BC)$$ lies in the interval $$0.23 \le x \le 0.48$$
PYP
IIT JEE 1983
Prove that the complex numbers $${{z_1}}$$, $${{z_2}}$$ and the origin form an equilateral triangle only if $$z_1^2 + z_2^2 - {z_1}\,{z_2} = 0$$.
PYP
IIT JEE 1983
The end $$A, B$$ of a straight line segment of constant length $$c$$ slide upon the fixed rectangular axes $$OX, OY$$ respectively. If the rectangle $$OAPB$$ be completed, then show that the locus of the foot of the perpendicular drawn from $$P$$ to $$AB$$ is $${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {c^{{2 \over 3}}}$$
PYP
IIT JEE 1983
Through a fixed point (h, k) secants are drawn to the circle $$\,{x^2}\, + \,{y^2} = \,{r^2}$$. Show that the locus of the mid-points of the secants intercepted by the circle is $$\,{x^2}\, + \,{y^2} $$ = $$hx + ky$$.
PYP
IIT JEE 1983
The coordinates of $$A, B, C$$ are $$(6, 3), (-3, 5), (4, -2)$$ respectively, and $$P$$ is any point $$(x, y)$$. Show that the ratio of the area of the triangles $$\Delta $$ $$PBC$$ and $$\Delta $$$$ABC$$ is $$\left| {{{x + y - 2} \over 7}} \right|$$
PYP
IIT JEE 1983
Find the coordinates of the point on the curve $$y = {x \over {1 + {x^2}}}$$
where the tangent to the curve has the greatest slope.
where the tangent to the curve has the greatest slope.
PYP
IIT JEE 1983
If $$\left( {a + bx} \right){e^{y/x}} = x,$$ then prove that $${x^3}{{{d^2}y} \over {d{x^2}}} = {\left( {x{{dy} \over {dx}} - y} \right)^2}$$
PYP
IIT JEE 1983
A particle moves in a circle of radius R. In half the period of revolution its displacement is ________ and distance covered is _________.
PYP
IIT JEE 1983
Show that $$1+x$$ $$In\left( {x + \sqrt {{x^2} + 1} } \right) \ge \sqrt {1 + {x^2}} $$ for all $$x \ge 0$$
PYP
IIT JEE 1983
The absorption of hydrogen by palladium is commonly known as ______.
PYP
IIT JEE 1983
3 g of a salt of molecular weight 30 is dissolved in 250 g of water. The molality if the solution is _____.
PYP
IIT JEE 1983
Elements of the same mass number but of different atomic numbers are known as ____.
PYP
IIT JEE 1983
A river is flowing from west to east at a speed of 5 meters per minute. A man on the south bank of the river, capable of swimming at 10 meters per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction
PYP
IIT JEE 1983
Rutherford's scattering experiment is related to the size of the
PYP
IIT JEE 1983
The principal quantum number of an atom is related to the
PYP
IIT JEE 1983
Any p-orbital can accommodate upto
PYP
IIT JEE 1983
Carbon tetrachloride has no net dipole moment because of
PYP
IIT JEE 1983
The types of bonds present in CuSO4.5H2O are only
PYP
IIT JEE 1983
Which one among the following does not have the hydrogen bond?
PYP
IIT JEE 1983
Heavy water is
PYP
IIT JEE 1983
The rational number, which equals the number $$2\overline {357} $$ with recurring decimal is
PYP
IIT JEE 1983
The coefficient of $${x^4}$$ in $${\left( {{x \over 2} - {3 \over {{x^2}}}} \right)^{10}}$$ is
PYP
IIT JEE 1983
The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram taken in order if and only if
PYP
IIT JEE 1983
Given positive integers $$r > 1,\,n > 2$$ and that the coefficient of $$\left( {3r} \right)$$th and $$\left( {r + 2} \right)$$th terms in the binomial expansion of $${\left( {1 + x} \right)^{2n}}$$ are equal. Then
PYP
IIT JEE 1983
The volume of the parallelopiped whose sides are given by
$$\overrightarrow {OA} = 2i - 2j,\,\overrightarrow {OB} = i + j - k,\,\overrightarrow {OC} = 3i - k,$$ is
$$\overrightarrow {OA} = 2i - 2j,\,\overrightarrow {OB} = i + j - k,\,\overrightarrow {OC} = 3i - k,$$ is
PYP
IIT JEE 1983
Fifteen coupons are numbered $$1, 2 ........15,$$ respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is $$9,$$ is
PYP
IIT JEE 1983
The points with position vectors $$60i+3j,$$ $$40i-8j,$$ $$ai-52j$$ are collinear if
PYP
IIT JEE 1983
From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is $${15^ \circ }$$. The distance of the boat from the foot of the light house is
PYP
IIT JEE 1983
The equation of the circle passing through (1, 1) and the points of intersection of $${x^2} + {y^2} + 13x - 3y = 0$$ and $$2{x^2} + 2{y^2} + 4x - 7y - 25 = 0$$ is
PYP
IIT JEE 1983
The straight lines $$x + y = 0,\,3x + y - 4 = 0,\,x + 3y - 4 = 0$$ form a triangle which is
PYP
IIT JEE 1983
The value of $$\tan \left[ {{{\cos }^{ - 1}}\left( {{4 \over 5}} \right) + {{\tan }^{ - 1}}\left( {{2 \over 3}} \right)} \right]$$ is
PYP
IIT JEE 1983
The centre of the circle passing through the point (0, 1) and touching the curve $$\,y = {x^2}$$ at (2, 4) is
PYP
IIT JEE 1983
The normal to the curve $$\,x = a\left( {\cos \theta + \theta \sin \theta } \right)$$, $$y = a\left( {\sin \theta - \theta \cos \theta } \right)$$ at any point $$'\theta '$$ is such that
PYP
IIT JEE 1983
If $$y = a\,\,In\,x + b{x^2} + x$$ has its extreamum values at $$x=-1$$ and $$x=2$$, then
PYP
IIT JEE 1983
If $$a+b+c=0$$, then the quadratic equation $$3a{x^2} + 2bx + c = 0$$ has
PYP
IIT JEE 1983
Use mathematical Induction to prove : If $$n$$ is any odd positive integer, then $$n\left( {{n^2} - 1} \right)$$ is divisible by 24.
PYP
IIT JEE 1983
$$AB$$ is a diameter of a circle and $$C$$ is any point on the circumference of the circle. Then
PYP
IIT JEE 1983
The value of the integral $$\int\limits_0^{\pi /2} {{{\sqrt {\cot x} } \over {\sqrt {\cot x} + \sqrt {\tan x} }}dx} $$ is
PYP
IIT JEE 1983
Match the physical quantities given in column I with dimension expressed in terms of mass (M), length (L), time (T), and charge (Q) given in column II and write the correct answer against the matched quantity in a tabular form in your answer book.
| Column I | Column II |
|---|---|
| Angular Momentum | ML2T-2 |
| Latent heat | ML2Q-2 |
| Torque | ML2T-1 |
| Capacitance | ML3T-1Q-2 |
| Inductance | M-1L-2T2Q2 |
| Resistivity | L2T-2 |
PYP
IIT JEE 1983
The density of a 3 M Sodium thiosulphate solution (Na2S2O3) is 1.25 g per ml. Calculate
(i) the percentage by weight of sodium thiosulphate,
(ii) the mole fraction of sodium thiosulphate and
(iii) the molalities of Na+ and $$S_2O_3^{-2}$$ ions
(i) the percentage by weight of sodium thiosulphate,
(ii) the mole fraction of sodium thiosulphate and
(iii) the molalities of Na+ and $$S_2O_3^{-2}$$ ions
PYP
IIT JEE 1983
Complete and balance the following equation:
HNO3 + HCl $$\to$$ NO + Cl2
HNO3 + HCl $$\to$$ NO + Cl2
PYP
IIT JEE 1983
Complete and balance the following equations:
Cl2 + OH- $$\to$$ Cl- + ClO-
Cl2 + OH- $$\to$$ Cl- + ClO-
PYP
IIT JEE 1983
Complete and balance the following equation:
Ce3+ + $$S_2O_8^{-2} \to $$ $$SO_4^{-2}$$ + Ce4+
Ce3+ + $$S_2O_8^{-2} \to $$ $$SO_4^{-2}$$ + Ce4+
PYP
IIT JEE 1983
Complete and balance the following equation:
$$Cr_2O_7^{2-}$$ + C2H4O $$\to$$ C2H4O2 + Cr3+
$$Cr_2O_7^{2-}$$ + C2H4O $$\to$$ C2H4O2 + Cr3+
PYP
IIT JEE 1983
Complete and balance the following equation:
Zn + $$NO_3^- \to$$ Zn2+ + $$NH_4^+$$
Zn + $$NO_3^- \to$$ Zn2+ + $$NH_4^+$$
PYP
IIT JEE 1983
An organic compound CxH2yOy was burnt with twice the amount of oxygen needed for complete combustion of CO2 and H2O. The hot gases when cooled to 0oC and 1 atm pressure, measured 2.24 litres. The water collected during cooling weighed 0.9 g. The vapour pressure of pure water at 20oC is 17.5 mm Hg and is lowered by 0.104 mm when 50 g of the organic compound are dissolved in 1000 g of water. Give the molecular formula of the organic compound.
PYP
IIT JEE 1983
Find all real values of $$x$$ which satisfy $${x^2} - 3x + 2 > 0$$ and $${x^2} - 2x - 4 \le 0$$
PYP
IIT JEE 1983
If $${\left( {1 + ax} \right)^n} = 1 + 8x + 24{x^2} + .....$$ then $$a=..........$$ and $$n =............$$
PYP
IIT JEE 1983
A vector $$\overrightarrow A $$ has components $${A_1},{A_2},{A_3}$$ in a right -handed rectangular Cartesian coordinate system $$oxyz.$$ The coordinate system is rotated about the $$x$$-axis through an angle $${\pi \over 2}.$$ Find the components of $$A$$ in the new coordinate system in terms of $${A_1},{A_2},{A_3}.$$
PYP
IIT JEE 1983
The area of the triangle whose vertices are $$A(1, -1, 2), B(2, 1, -1), C(3, -1, 2)$$ is ..........
PYP
IIT JEE 1983
The unit vector perpendicular to the plane determined by $$P\left( {1, - 1,2} \right),\,Q\left( {2,0, - 1} \right)$$ and $$R\left( {0,2,1} \right)$$ is ...........
PYP
IIT JEE 1983
Show that $$$16\cos \left( {{{2\pi } \over {15}}} \right)\cos \left( {{{4\pi } \over {15}}} \right)\cos \left( {{{8\pi } \over {15}}} \right)\cos \left( {{{16\pi } \over {15}}} \right) = 1$$$
PYP
IIT JEE 1983
Find all solutions of $$4{\cos ^2}\,x\sin x - 2{\sin ^2}x = 3\sin x$$
PYP
IIT JEE 1983
Find all the solution of $$4$$ $${\cos ^2}x\sin x - 2{\sin ^2}x = 3\sin x$$
PYP
IIT JEE 1983
The vertices of a triangle are
$$\left[ {a{t_1}{t_2},\,\,a\left( {{t_1} + {t_2}} \right)} \right],\,\,\left[ {a{t_2}{t_3},a\left( {{t_2} + {t_3}} \right)} \right],\,\,\left[ {a{t_3}{t_1},\,a\left( {{t_3} + {t_1}} \right)} \right]$$. Find the orthocentre of the triangle.
$$\left[ {a{t_1}{t_2},\,\,a\left( {{t_1} + {t_2}} \right)} \right],\,\,\left[ {a{t_2}{t_3},a\left( {{t_2} + {t_3}} \right)} \right],\,\,\left[ {a{t_3}{t_1},\,a\left( {{t_3} + {t_1}} \right)} \right]$$. Find the orthocentre of the triangle.
PYP
IIT JEE 1983
Given the points $$A\left( {0,4} \right)$$ and $$B\left( {0, - 4} \right)$$, the equation of the locus of the point $$P\left( {x,y} \right)$$ such that $$\left| {AP - BP} \right| = 6$$ is .............
PYP
IIT JEE 1983
The point of intersection of the line 4x - 3y - 10 = 0 and the circle $${x^2} + {y^2} - 2x + 4y - 20 = 0$$ are ........................and ...................
PYP
IIT JEE 1983
The function $$y = 2{x^2} - In\,\left| x \right|$$ is monotonically increasing for values of $$x\left( {x \ne 0} \right)$$ satisfying the inequalities ......... and monotonically decreasing for values of $$x$$ satisfying the inequalities ............
PYP
IIT JEE 1983
The larger of $$\cos \left( {In\,\,\theta } \right)$$ and $$In $$ $$\left( {\cos \,\,\theta } \right)$$ If $${e^{ - \pi /2}} < \theta < {\pi \over 2}$$ is ..................
PYP
IIT JEE 1983
Evaluate : $$\int {{{\left( {x - 1} \right){e^x}} \over {{{\left( {x + 1} \right)}^3}}}dx} $$
PYP
IIT JEE 1983
Evaluate : $$\int\limits_0^{\pi /4} {{{\sin x + \cos x} \over {9 + 16\sin 2x}}dx} $$
PYP
IIT JEE 1983
Find the area bounded by the $$x$$-axis, part of the curve $$y = \left( {1 + {8 \over {{x^2}}}} \right)$$ and
the ordinates at $$x=2$$ and $$x=4$$. If the ordinate at $$x=a$$ divides the area into two equal parts, find $$a$$.
the ordinates at $$x=2$$ and $$x=4$$. If the ordinate at $$x=a$$ divides the area into two equal parts, find $$a$$.
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